I think a point some of us are trying to make is, that some places communicate via things other then an official, outright statement or policy that children aren't welcome. Ambiance, tone, etc are supposed to be clues as to the audience the establishment is aiming for.
Take NYC's famous 21 Club. No where on the website, or to my recollection the menu or signage in the lobby, does it say children are not permitted. But it is very much not, in my opinion or experience, a place appropriate for youngsters. Maybe a well behaved 10 year old, but not a 4 year old who can sit in an adult chair, but who is still none the less only 4.
Wines are not ordered via a waiter, but rather via the sommelier, 3-4 courses are the norm per person (these are not over-sized appetizers meant to be shared, or overly large entrees fit for half to be immediately wrapped up - such as one might get at TGIFridays or Outback), men are required to wear jackets and sneakers are not permitted, etc. So while there is no (that I know of) official policy on children, its not a stretch to read between the lines and realize it is not a place children are welcome. Officially they might be allowed, but allowed does not equal welcomed.